An Introduction to Default Logic

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Springer Science & Business Media, Sep 29, 1989 - Computers - 208 pages
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This book is written for those who are interested in a fonnalization of human reasoning, especially in order to build "intelligent" computer systems. Thus, it is mainly designed for the Artificial Intelligence community, both students and researchers, although it can be useful for people working in related fields like cognitive psychology. The major theme is not Artificial Intelligence applications, although these are discussed throughout in sketch fonn. Rather, the book places a heavy emphasis on the fonnal development of default logic, results and problems. Default logic provides a fonnalism for an important part of human reasoning. Default logic is specifically concerned with common sense reasoning, which has recently been recognized in the Artificial Intelligence literature to be of fundamental importance for knowledge representation. Previously, fonnalized reasoning systems failed in real world environments, though succeeding with an acceptable ratio in well-defined environments. This situation enabled empirical explorations and the design of systems without theoretical justification. In particular, they could not be compared since there was no basis to judge their respective merits. Default logic turned out to be very fruitful by proving the correctness of some of them. We hope that this book will initiate other successful developments in default logic.
  

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Contents

Default Reasoning
1
12 Default Reasoning
3
Formal Logic as a Knowledge Representation Scheme
5
Syntactical Part
6
Semantical Part
8
24 Properties for Formal Logic
9
25 Logical Languages for Knowledge Representation
11
First Order Logic
13
Default Logic Revisited
111
112 Modified Extensions
113
113 Lukaszewicz ProofTheoretic Approach to Default Logic
119
114 Lukaszewicz ModelTheoretic Approach to Default Logic
123
115 The BeliefsJustifications Pairs Setting
124
116 Default Logic Revisited Versus Default Logic?
128
Circumscription
131
122 Model Theory for Predicate Circumscription
135

32 First Order Model Theory
19
33 First Order Proof Theory
22
34 Properties of First Order Logic
25
Nonmonotonic Extensions for First Order Logic
27
42 Retaining the Advantages of First Order Logic
29
Presentation of Default Logic
31
Formal Development of Default Logic
37
62 General Properties of Default Theories
44
Normal Defaults
53
72 Default Proof Theory
60
73 Default Model Theory
67
74 Completeness and Decidability Matters
74
Further Topics in Default Logic
75
82 Interacting Defaults
80
Fragments of Default Logic
89
92 SemiNormal Default Theories
94
93 Taxonomic Default Theories
99
Problems with Default Logic
101
102 Undesirable Features of Default Logic
108
123 Existence of Minimal Models
141
124 Equality and Predicate Circumscription
146
125 Joint Predicate Circumscription
149
126 First Order Formula Circumscription
153
127 Second Order Formula Circumscription
155
128 Prioritized Formula Circumscription
158
129 Pointwise Circumscription
160
Other Logic Formalizations of Nonmonotonic Reasoning
163
132 Intuitionistic Nonmonotonic Logic
167
133 Modal Nonmonotonic Logic for Axiomatic Default Theories
170
134 ThreeValued Nonmonotonic Logic
172
135 Autoepistemic Logic
174
136 The Logic of Theory Change
189
137 Logic Systems for Belief Revision
192
Origin of the Theorems
193
References
195
Table of Symbols
203
Index
205
Copyright

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About the author (1989)

Philippe Besnard is CNRS (Centre National de la Recherche Scientifique) Research Director in the Logic, Interaction, Language, and Computation Group of the Institut de Recherche et Informatique Toulouse at UniversitA(c) Paul Sabatier.